How to lock to desired axis permanently in edit mode
If you're using hotkeys to translate your vertices, the fastest way to work is to use the middle-click shortcut:


Press G to begin your grab operation and begin moving your selection roughly along the axis you want to lock to.
Now, middle-click and you'll be locked to that axis.


Alternatively, you can hold the middle mouse button down (again, while still in the Grab operation) and you'll see lock guides in the 3D View. While still holding the middle mouse button, you can drag your selection to lock to one of these axes. When you release the middle mouse button, the lock remains in place.

Both methods also work with the right-click-and-drag "tweak mode" way of initiating the Grab operator.